In the past few years, we have witnessed an increased interest in the use of 2D materials for the realization of hybrid photonic nonlinear waveguides. Although graphene has attracted most of the attention, other families of 2D materials such as transition metal dichalcogenides have also shown promising nonlinear performances. In this work, we propose a strategy for designing silicon nitride waveguide structures embedded with MoS2 for nonlinear applications. The transverse geometry of the hybrid waveguide's structure is optimized for high third-order nonlinear effects using optogeometrical engineering and multiple layers of MoS2. Stacking multiple monolayers, results in an improvement of 2 orders of magnitude in comparison with standard silicon nitride waveguides. The performance of the hybrid waveguides is then investigated in terms of four-wave mixing enhancement in micro-ring resonator configurations. A -6.3 dB signal/idler conversion efficiency is reached around 1.55µm wavelength for a 5 mW pumping level.
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